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Principle of Proportionality

This is a short article on the principle of proportionality. The principle states that if the state space is partitioned into equally likely events, \(A_1\), \(A_2\), \(\ldots A_n\) and if \(B\) is another event, then \(P(A_i | B)\) is proportional to \(P(B | A_i)\). The principle is derived from Bayes' theorem, and applications are given to a bear cub problem, a pancake problem, and the Monty Hall problems.